Electrical circuits RC and RL involving fractional operators with bi-order

• Main Authors: JF Gómez-Aguilar, RF Escobar-Jiménez, VH Olivares-Peregrino, MA Taneco-Hernández, GV Guerrero-Ramírez
• Format: Article
• Language: English
• Published: SAGE Publishing 2017-06-01
• Series: Advances in Mechanical Engineering
• Online Access: https://doi.org/10.1177/1687814017707132

This article describes electrical series circuits RC and RL using the concept of derivative with two fractional orders α and β in Liouville–Caputo sense. The fractional equations consider derivatives in the range of α , β ∈ ( 0 ; 1 ] . Numerical solutions are presented considering different source terms introduced in the fractional equation. This new approach considers electrical elements with two different properties. In addition, we prove that if α = 0 , the fractional derivative with Mittag-Leffler kernel in Liouville–Caputo sense is recovered, and when β = 0 , the Liouville–Caputo fractional derivative is recovered.